Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 171
from the Stoics, not from Aristotle; Boethius wrote about them, and they formed
a standard part of the curriculum. They typically included six types:
Conjunctions
Disjunctions
Conditionals
Causals
Temporal Propositions
Locational Propositions
Conjunctions and disjunctions are just what one expects; they are combinations of
propositions made with ‘and’ (et) and ‘or’ (vel), or similar words. A conjunction
is true iff both of its conjuncts are true, and false if either or both are false; a
disjunction is true iff either or both of its disjuncts are true, and false if both
disjuncts are false. So they were given modern truth conditions, even including
the fact that ‘or’ was usually treated inclusively. 16
Conditionals are made with ‘if’ (si), or equivalent words. A conditional was
usually taken to be true if it is necessary that the antecedent not be true without
the consequent also being true. 17 This makes the truth of a conditional equivalent
to the goodness of the related consequence, as some writers observed. 18 Some
authors also discuss “ut nunc” (as of now) conditionals, which are equivalent to
our material implication. 19 But the default meaning of a conditional is that it is
true if it is impossible for the antecedent to be true and the consequent false.
Causal propositions are those made by linking two propositions with ’because’
(quia) or an equivalent word. Such a causal proposition is true if the one proposition
causes the other. However, ‘cause’ must not be read here as efficient causation;
it is more like a version of ‘because’. An example of such a proposition is ‘Because
Socrates is a man, Socrates is an animal’. [Ockham SL II.34]
A temporal proposition is made from smaller propositions using ‘while’ or ’when’
(dum, quando), and a locational proposition is one using ‘where’ (ubi). The former
is said to be true if both component propositions are true for the same time. The
latter is true if the location of the event mentioned in the one proposition is the
same as that in the other. These, along with causal propositions, employ notions
that are not part of the basic theory discussed here.
16 Sherwood SW XXI.1 (141) holds that “. . . ‘or’ is taken sometimes as a disjunctive and
at other times as a subdisjunctive. In the first case it indicates that one is true and the other is
false; in the second case it indicates solely that one is true while touching on nothing regarding
the other part.” Later, Paul of Venice LP I.14 (132) clearly gives inclusive truth conditions:
“For the truth of an affirmative disjunctive it is required and it suffices that one of the parts is
true; e.g. ‘you are a man or you are a donkey’. For the falsity of an affirmative disjunctive it is
required that both parts be false; e.g., ‘you are running or no stick is standing in the corner’.”
17 Ockham SL II.31; Peter of Spain T I.17. Sherwood IL I.18 gives truth conditions that are
not clearly modal: “whenever the antecedent is [true], the consequent is [true].”
18 Ockham ibid.
19 Cf Buridan TC I.4.7-7.12. He noted, e.g., that “if the antecedent is false, though not
impossible, the consequence is acceptable ut nunc”.